Whakaoti i te a^2+a=7

$$a ^ { 2 } + a = 7$$

Whakaoti mō a

$$a = \frac{\sqrt{29} - 1}{2} \approx 2.192582404$$

$$a=\frac{-\sqrt{29}-1}{2}\approx -3.192582404$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$a^{2}+a=7$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$a^{2}+a-7=7-7$$

Mā te tango i te 7 i a ia ake anō ka toe ko te 0.

$$a^{2}+a-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-1±\sqrt{1^{2}-4\left(-7\right)}}{2}$$

Pūrua 1.

$$a=\frac{-1±\sqrt{1-4\left(-7\right)}}{2}$$

Whakareatia -4 ki te -7.

$$a=\frac{-1±\sqrt{1+28}}{2}$$

Tāpiri 1 ki te 28.

$$a=\frac{-1±\sqrt{29}}{2}$$

Nā, me whakaoti te whārite a=\frac{-1±\sqrt{29}}{2} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{29}.

$$a=\frac{\sqrt{29}-1}{2}$$

Nā, me whakaoti te whārite a=\frac{-1±\sqrt{29}}{2} ina he tango te ±. Tango \sqrt{29} mai i -1.

$$a=\frac{-\sqrt{29}-1}{2}$$

Kua oti te whārite te whakatau.

$$a=\frac{\sqrt{29}-1}{2} a=\frac{-\sqrt{29}-1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$a^{2}+a=7$$

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}+a+\left(\frac{1}{2}\right)^{2}=7+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}+a+\frac{1}{4}=7+\frac{1}{4}$$

Tāpiri 7 ki te \frac{1}{4}.

$$a^{2}+a+\frac{1}{4}=\frac{29}{4}$$

Tauwehea a^{2}+a+\frac{1}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(a+\frac{1}{2}\right)^{2}=\frac{29}{4}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(a+\frac{1}{2}\right)^{2}}=\sqrt{\frac{29}{4}}$$

Whakarūnātia.

$$a+\frac{1}{2}=\frac{\sqrt{29}}{2} a+\frac{1}{2}=-\frac{\sqrt{29}}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$a=\frac{\sqrt{29}-1}{2} a=\frac{-\sqrt{29}-1}{2}$$